Antenna and Propagation Dr. Moazam Maqsood moazam@ist.edu.pk

Spacecraft DesignDr. Moazam Maqsoodmoazam@ist.edu.pkAttitude Control System (ACS)5/4/20151Attitude Control System (ACS)Feedback Control SystemAttitude measurement through sensorsAttitude correction through actuatorsControl system or control law

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Attitude Control SystemDisturbances that make attitude control necessaryTorques from solar pressureAerodynamicsMagnetic fieldsGravity gradientsSpacecraft activities

5/4/20153Spin-Stabilized SystemTakes advantage of inherent resistance of spinning bodyNo disturbance Momentum vector remains fixed in inertial spaceDisturbance vector parallel to momentum axis causes spin rate to changeDisturbance vector parallel to momentum axis causes momentum vector to precess

5/4/20154Spin-Stabilized SystemAdvantagesSimple, Low costThrust vector control is not requiredSpinning supplies scanning motion; necessary for some instrumentsDisadvantagePointing accuracy is lowTight control of moment of inertia is requiredOnly possible location for solar panels is spinning body exterior; the area is not exposed to sun all the time (32%) 5/4/20155Dual-Spin SystemImproves the pointing accuracy of spin stabilized systemOffers the advantages of a spin stabilized systemDespin drive assembly is expensive and failure prone5/4/20156

Three-Axis Stabilized SystemA typical system uses gyros as inertial reference and updates them periodically using star scanning or horizon scanningAttitude errors are removed using reaction wheelsThrusters are used to provide positive or negative translations5/4/20157Three-Axis Stabilized SystemAdvantagesUnlimited pointing capabilityBest possible pointing accuracy (>0.001 deg)Solar panel location and size is not restrictedCan be oriented to illuminate maximum solar panel areaDisadvantagesComplex, Heavy and High power consumptionMore chances of system failureThrust vector controlling is requiredRedundancy is required

5/4/20158Gravity-Gradient SystemAligns the spacecraft long vector to the gravity vectorGravity gradient torques should be greater than any other disturbancesMoment of inertia about any 2 axes should be greater than moment about 3rd axisCan be used only under 1000 kmUseful when long life and high reliability are required5/4/20159Gravity gradient stabilization5/4/201510

Momentum Bias SystemsUses a momentum wheel to provide stiffness in two axes, control in the third oneUseful for Nadir pointingSimple and cheaperManeuvering capability is very limited5/4/201511Disturbance TorquesSolar Torque (35000 km and above)Momentum exchange between a solar photon and the spacecraftMagnetic Torque (500 to 35000 km)Magnetic field of earth and other celestial bodiesGravity Gradient Torque (500 to 35000 km)Imbalance of gravitational pull on the spacecraftAerodynamic Drag (< 500 km)Source of torque as well as velocity reduction in LEO5/4/201512Solar TorqueMomentum exchange between the solar photon and spacecraftA force is exerted on the surfaceAbsorptionForce will be aligned with the sun vectorSpecular reflectionForce exerted is normal to the surfaceDiffuse reflectionAbsorption and reradiation distributed uniformly over a hemisphereNet force is exerted normal to the surface5/4/201513Solar TorqueAbsorption

Specular reflection

Diffuse reflection

Ps = Is/cIs = Incident solar pressure (1376 W/m2)Ps = solar pressure (N/m2)5/4/201514q = 0 is absorber, q = 1 is pure reflector, normal value = 0.5, 0.614Example 5.1Ts = ?Solar panel = 9 m2Spacecraft = 1 m2Attaching Boom = 0.25 mAngle b/w Sun vector and spacecraft normal = 20 degq = 0.3

5/4/201515Magnetic Torque5/4/201516Magnetic Torque5/4/201517Earth magnetic field5/4/201518Example 5.2Spacecraft residual dipole = 2 A-m2Altitude = 400 km in equatorial orbitMagnitude of Magnetic moment = ?5/4/201519Gravity Gradient Torque5/4/201520Example 5.3Estimate the gravity gradient torque on SkylabMass = 90,505 kgHeight = 35 mDiameter = 5.4 mRadius = 2.7 mAltitude = 442 kmRadius = 5820 kmAttitude error = 5 deg (0.087266 rad)Iz = Wr2/2 , Ix,y = W(3r2+h2)/125/4/201521Aerodynamic Drag5/4/201522Example 5.4400 km circular orbitDrag force on 9 m2 solar panel = ?Velocity at 400 km = 7.669 km/sAtm. Density = 1.2 x 10-11 kg/m35/4/201523Spacecraft Generated TorquesPointing rotation of solar panels / antennas / camerasDeployment of solar panels / antennasPropellant sloshFlexible appendagesReaction wheel imbalance

5/4/201524System SizingActuator sizing is dependent upon the combined magnitude of disturbance torquesActuator must have sufficient authority to counteract the disturbanceAn actuator with twice the capability of disturbance torques would have 100% control authorityOnce the actuators are decided the required resources for the mission life must be analyzed 5/4/201525Attitude Determination MethodsSpacecraft axes must be located with respect to a reference frame+Z axis is anti-Nadir (parallel to r)+X axis in direction of motion (parallel to V)+Y axis (parallel to r x V direction)Euler anglesRelationship between reference frame and the spacecraft frame are defined by three rotation angles 5/4/201526Attitude Determination Methods5/4/201527

Euler AnglesSet of three angles and a sequence of rotation such that one coordinated system can be rotated into anotherBoth magnitude and sequence of rotation are importantAltering the sequence can change the resulting rotation12 different Euler sets result in the same relative position5/4/201528Euler Angles

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Direction Cosine Matrix (DCM)5/4/201530

DCM to Euler angles5/4/201531

Disadvantage of DCMPerforming a rotation requires27 Multiplications15 Additions29 Trigonometric EvaluationsRequire large memory and intensive computations

Use Quaternions5/4/201532Quaternions5/4/201533